math

Tamás TITKOS

Contact information

Corvinus University of Budapest, Department of Mathematics
H-1093 Budapest, Fővám tér 13-15.
E-mail: tamas.titkos@uni-corvinus.hu
Office: Salt House, S229a

and

HUN-REN Alfréd Rényi Institute of Mathematics
H-1053 Budapest, Reáltanoda utca 13-15.
E-mail: titkos@renyi.hu
Office: III/16

Research interests

• Functional analysis
• Optimal transport and Wasserstein spaces
• Lipschitz-free spaces
  
  

Awards, Scholarships

• Bolyai Memorial Certificate for “Excellent” Research Performance (2022)
• Alexits Prize of the Hungarian Academy of Sciences (2021)
• BBU Science Award (2020)
• Bolyai+ Scholarship - New National Excellence Programme (2018,2019,2020)
• János Bolyai Research Fellowship (2018)
• Youth Award of the Hungarian Academy of Sciences (2018)
• NRDI Postdoctoral Fellowship (2018)
  
  

Editorial work

• Editor of Periodica Mathematica Hungarica
• Editor of Érintő (Electronic Journal of the János Bolyai Mathematical Society)
  
  

Recent Manuscripts

1. On the metric property of quantum Wasserstein divergences (with G. Bunth, J. Pitrik, and D. Virosztek)
   [to appear in Physical Review A]

2. Isometries of Lipschitz-free Banach spaces (with M. Cúth and M. Doucha)
   [to appear in the Journal of the London Mathematical Society]

3. Isometric rigidity of Wasserstein spaces over Euclidean spheres (with Gy.P. Gehér, A. Hrušková, and D. Virosztek)
   [to appear in the Journal of Mathematical Analysis and Applications]

4. Isometric rigidity of the Wasserstein space W₁(G) over Carnot groups (with Z.M. Balogh and D. Virosztek)

5. Isometries and isometric embeddings of Wasserstein spaces over the Heisenberg group (with Z.M. Balogh and D. Virosztek)

6. Lattice properties of strength functions (with A. Ramanantoanina)
   [to appear in Acta Scientiarum Mathematicarum]

A Book

Jan Maas, Simone Rademacher, Tamás Titkos, Dániel Virosztek (Eds.)
Optimal Transport on Quantum Structures
Part of the book series: Bolyai Society Mathematical Studies (BSMS, volume 29)

Selected Papers

1. On the exotic isometry flow of the quadratic Wasserstein space over the real line
   Linear Algebra and its Applications, 2024
   DOI: https://doi.org/10.1016/j.laa.2023.02.016 (with Gy.P. Gehér and D. Virosztek)

2. Quantum Wasserstein isometries on the qubit state space
   Journal of Mathematical Analysis and Applications, 2023
   DOI: https://doi.org/10.1016/j.jmaa.2022.126955 (with Gy.P. Gehér, J. Pitrik, and D.Virosztek)

3. Isometric rigidity of Wasserstein spaces: the graph metric case
   Proceedings of the American Mathematical Society, 2022
   DOI: https://doi.org/10.1090/proc/15977 (with G. Kiss)

4. The isometry group of Wasserstein spaces: the Hilbertian case
   Journal of the London Mathematical Society, 2022
   DOI: https://doi.org/10.1112/jlms.12676 (with Gy.P. Gehér and D. Virosztek)

5. Isometric study of Wasserstein spaces - the real line
   Transactions of the American Mathematical Society, 2020
   DOI: https://doi.org/10.1090/tran/8113 (with Gy.P. Gehér and D. Virosztek)

6. Operators on anti-dual pairs: Generalized Krein-von Neumann extension
   Mathematische Nachrichten, 2020
   DOI: https://doi.org/10.1002/mana.201800431 (with Zs. Tarcsay)

7. Arlinskii’s iteration and its applications
   Proceedings of the Edinburgh Mathematical Society, 2019
   DOI: https://doi.org/10.1017/S0013091518000287

8. A characterisation of isometries with respect to the Lévy-Prokhorov metric
   Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, 2019
   DOI: https://doi.org/10.2422/2036-2145.201702_011) (with Gy.P. Gehér)

9. A Simple Proof of the Lebesgue Decomposition Theorem
   The American Mathematical Monthly, 2015
   DOI: https://doi.org/10.4169/amer.math.monthly.122.8.793

10. A Radon-Nikodym type theorem for forms
    Positivity, 2013
    DOI: https://doi.org/10.1007/s11117-012-0209-1 (with Z. Sebestyén)

Selected talks

• 11/07/2016 Surjective Lévy-Prokhorov isometries
  20th Conference of the International Linear Algebra Society
  Leuven, Belgium

• 15/08/2017 Lebesgue decomposition and order structure
  International Workshop on Operator Theory and its Applications
  Chemnitz, Germany

• 21/11/2017 Lebesgue- and Radon–Nikodym type theorems
  Formal Sciences Seminar, IST Austria
  Klosterneuburg, Austria

• 28/11/2017 Extension of suboperators and the generalized Schur complement
  Functional Analysis Seminar, University of Oxford
  Oxford, United Kingdom

• 19/06/2018 Characterisations of isometries with respect to probability distances
  Preservers: Modern Aspects and New Directions, Queen’s University Belfast
  Belfast, Northern Ireland

• 12/07/2018 Generalized Krein - von Neumann extension
  6th Summer Workshop on Operator Theory, Uniwersytet Rolniczy w Krakowie
  Kraków, Poland
  

• 19/12/2018 Positive operators on anti-dual pairs
  2018 China-Korea International Conference on Matrix Theory with Applications, Shanghai University
  Shanghai, China

• 29/01/2019 On the isometry group of metric spaces of probability measures
  Researches on isometries as preserver problems and related topics, Kyoto RIMS
  Kyoto, Japan

• 08-12/07/2019 Positive operators on anti-dual pairs: Parallel addition
  ILAS 2019 - Invited Mini-Symposium: Matrix Analysis
  Rio de Janeiro, Brasil

• 17/02/2020 Isometries of Wasserstein spaces
  Rings, Modules and Matrices Seminar, Lomonosov Moscow State University
  Moscow, Russia

• 17/11/2020 Isometries of Wasserstein spaces
  Analysis Seminar, University of Wisconsin-Madison Madison, United States [via Zoom]

• 20-26/06/2021 Maps preserving absolute continuity of positive operators
  8th European Congress of Mathematics
  Portoroz, Slovenia

• 23/11/2022 On the Monge-Kantorovich distance over concave base spaces
  Real and Abstract Analysis Seminar, Charles University
  Prague, Czech Republic

• 18/09/2023 On exotic isometries of Wasserstein spaces
  Séminaire de Mathématiques et Colloquium, Institut de Recherche en Informatique, Mathématiques, Automatique et Signal
  Mulhouse, France

• 20/09/2023 Isometries of Wasserstein spaces and Lipschitz-free spaces
  Æsy to define, Hard to analyse: First conference on Lipschitz-free spaces, Centre Diocésain
  Besançon, France

• 16/07/2024 Isometries and isometric embeddings of Wasserstein spaces over the Heisenberg group
  9th European Congress of Mathematics
  Sevilla, Spain

• 15/08/2024 Lattice properties of strength functions
  35th International Workshop on Operator Theory and its Applications
  Canterbury, United Kingdom

• 02/09/2024 Quantum Wasserstein isometries on the qubit state space
  INdAM Meeting - Quantum Optimal Transport and Applications, Palazzone di Cortona
  Cortona, Italy

Ph.D. Thesis

Decomposition theory of forms, 2016
Doctoral School of Mathematics, Eötvös Loránd University

Participation in scientific grants/projects

• 2016/02-2017/08
  K104206 (National Research, Development and Innovation Office), “Research and application of matrices”
  (Principal Investigator: Máté Matolcsi)

• 2018/09–2019/06
  ÚNKP-18-4-BGE-3 (Bolyai+ Scholarship for Young Higher Education Teachers and Researchers), “Investigation of shorted parts”

• 2018/09–2021/08
  PD128374 (National Research, Development and Innovation Office), “Extension- and preserver problems”

• 2019/04–2020/08
  K115383 (National Research, Development and Innovation Office), “Operators, matrices and their structures”
  (Principal Investigator: Lajos Molnár)

• 2018/09–2021/08
  BO/00137/18/3 (MTA János Bolyai Research Scholarship), “Investigation of spaces of Borel probability measures and their isometry group”

• 2019/09–2020/06
  ÚNKP-19-4-BGE-1 (Bolyai+ Scholarship for Young Higher Education Teachers and Researchers), “Embeddings of Wasserstein spaces”

• 2020/12–2024/11
  K134944 (National Research, Development and Innovation Office), “Preservers on structures of operators and measures”
  (Principal Investigator: Lajos Molnár)

• 2020/09–2021/08
  ÚNKP-1-4-BGE-3 (Bolyai+ Scholarship for Young Higher Education Teachers and Researchers, “Optimal transport on graphs”

• 2021/09–2026/08
  LP2021-15/2021 (Momentum Program of the HAS), MTA RI “Momentum” Optimal Transport and Quantum Information Geometry Research Group
  (Principal Investigator: Dániel Virosztek)

• 2021/09–2023/08
  Renyi-ELKH-sa-70-2021 (Eötvös Loránd Research Network), “Transport distances on classical and quantum structures”
  

Memberships

• Public body of the Hungarian Academy of Sciences
• János Bolyai Mathematical Society
• European Mathematical Society
• American Mathematical Society
  
  

Organization of Academic Events

• Preserver Weekend in Szeged, 2019
  (with L. Molnár)

• Analysis Seminar of the Alfréd Rényi Institute of Mathematics, 2019-2020

• Preserver Webinar - an online seminar series on preserver problems, 2020
  (with Gy.P. Gehér and D. Virosztek)

• Functional Analysis and Operator Theory Webinar – with an emphasis on preserver problems and quantum information, 2020-21
  (with Gy.P. Gehér and D. Virosztek)

• Thematic semester at Erdős Cender (2022 Fall, Sept-Dec): Optimal Transport on Quantum Structures
  (with J. Maas, S. Rademacher and D. Virosztek)

  • School: Sept 19-23, 2022
    Lecturers: E.A. Carlen (Rutgers University), A. Figalli (ETH Zurich), F. Golse (CMLS Ecole Polytechnique), D. Trevisan (University of Pisa)

  • Workshop: Sept 26-30, 2022
    Invited speakers: P. Antonini (Università del Salento), Z. Balogh (University of Bern), Y. Brenier (Universite Paris-Saclay), A. Capel (Universität Tübingen), E. Caglioti (Sapienza University of Rome), Li Chen (University of Mannheim, Germany), N. Datta (University of Cambridge), G. De Palma (University of Bologna), M. Eckstein (Jagiellonian University), M. Iacobelli (ETH Zurich), L. Lafleche (UT Austin), L. Portinale (Hausdorff Center for Mathematics Bonn), C. Rouzé (TU Munich), D. Shlyakhtenko (UCLA), M. Wirth (IST Austria) H. Zhang (IST Austria), K. Zyczkowski (Polish Academy of Sciences)

  • Focus event on Modified Logarithmic Sobolev Inequalities for Quantum Markov Semigroups: November 21-25, 2022
    Ivan Bardet (Inria de Paris, France) Angela Capel (Universität Tübingen, Germany)
    Cambyse Rouzé (Technische Universität München, Germany), Daniel Stilck França (ENS Lyon, France)

  • Focus Event on the Geometry of Wasserstein Spaces: November 28 - December 2, 2022
    Ramón J. Aliaga (Universitat Politècnica de València), Zoltán Balogh (University of Bern, Switzerland)
    Nicolas Juillet (Université de Haute-Alsace), Eva Pernecká (Czech Technical University in Prague)

• “Big Five Centenary” - a mini-conference honoring the achievements of five outstanding Hungarian mathematicians born 100 years ago: János Aczél, Ákos Császár, László Fuchs, István Gál, and János Horváth – (local organizer)